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Rotating Ellipses

Two apps exploring rotating, tangent ellipses.

Tags: Ellipses, tangents, rotating

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Rotating Ellipses
Rotating Ellipses
Two ellipses rotate within a third such that the two smaller ellipses are always tangent to each other and the larger ellipse. Adjusting the variable X demonstrates this rotation. All three ellipses are constrained only by their implicit equations, and the moving ellipses' equations include functions of X that allow them to rotate. Can you figure out what the equations are (the other constants in the equations are a, b, h, and k)?

Tags: Ellipses, conics, puzzler

Rotating Ellipses with Arcs
Rotating Ellipses with Arcs
Now that you know how two ellipses can rotate such that they are tangent to each other and a third larger ellipse (see this app); the next challenge is to figure out how an arc placed on each ellipse can be constrained (with proportional points along the ellipses) such that each arc always covers half of the ellipse and one endpoint is on the tangent point of the two smaller ellipses.

Tags: Ellipses, conics, puzzler, arcs


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